Thresholding of Wavelet Coefficients as Multiple Hypotheses Testing Procedure

Abramovich, Felix; Benjamini, Yoav

doi:10.1007/978-1-4612-2544-7_1

Cited by 61 publications

(75 citation statements)

References 2 publications

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“…Neter,et al [6] menggunakan uji hipotesis untuk mengetahui signifikan atau tidaknya setiap koefisien regresi untuk memutuskan apakah koefisien-koefisien dalam regresi signifikan atau tidak. Dengan cara seperti ini, Abramovich dan Benjamini [1] menguji semua koefisien wavelet. Jika dalam uji hipotesis menyimpulkan bahwa koefisien wavelet signifikan maka koefisien ini akan dipertahankan dalam merekonstruksi fungsi tetapi kalau dalam uji hipotesis koefisien wavelet memutuskan sama dengan nol maka koefisien ini akan diabaikan.…”

Section: Pemilihan Parameter Thresholdingunclassified

Pemilihan Parameter Threshold Optimal Dalam Estimator Regresi Wavelet Thresholding Dengan Prosedur False Discovery Rate (Fdr)

Suparti¹,

Tarno²,

Haryono³

2012

Medstat

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If X is predictor variable and Y is response variable of following model Y = f (X) +e with function f is regression which not yet been known and e is independent random variable with mean 0 and variant 2 σ , hence function of f can estimate with parametric and nonparametric approach.At this paper estimate f with nonparametric approach. Nonparametric approach that used is wavelet shrinkage or wavelet thresholding method. At function estimation with method of wavelet thresholding, what most dominant determine level of smoothing estimator is value of threshold. The small threshold give function estimation very no smoothly, while the big value of threshold give function estimation very smoothly. Therefore require to be selected value of optimal threshold to determine optimal function estimation.One of the method to determine the value of optimal threshold is with procedure of False Discovery Rate ( FDR). In procedure of FDR, the optimal threshold determined by selection of level of significance. Smaller mount used significance progressively smoothly its .

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Section: Pemilihan Parameter Thresholdingunclassified

Pemilihan Parameter Threshold Optimal Dalam Estimator Regresi Wavelet Thresholding Dengan Prosedur False Discovery Rate (Fdr)

Suparti¹,

Tarno²,

Haryono³

2012

Medstat

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“…This scheme is characterised by a single parameter u: Thresholding schemes can be derived from various theoretical bases [26,27,[39][40][41]. If one retains the assumption of Gaussianity on the noise but considers various distributions for the underlying image, one can define various optimal thresholding schemes.…”

Section: Thresholding Schemesmentioning

confidence: 99%

“…The non-linear function used is selected from a parameterised family of functions, termed a scheme. The most widely used schemes are the soft-and hard-thresholding functions [23 -27], even if other schemes have been described in literature [27,41,42,45,46,50,51]. The value of parameters used to select the member of the scheme should depend on the statistics of signal and noise.…”

Section: Introductionmentioning

confidence: 99%

Film grain reduction on colour images using undecimated wavelet transform

Stefano

White

Collis

2004

Image and Vision Computing

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“…Wavelets, as being a powerful tool of signal processing, have been largely used in many signal processing domains and particularly in signal denoising: [23,24,25,26,27,28]. They have also been used in inverse problems: [29,30,31].…”

Section: Introductionmentioning

confidence: 99%

Wavelet Domain Image Separation

Mohammad‐Djafari¹,

Ichir

2003

AIP Conference Proceedings

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Abstract. In this paper, we consider the problem of blind signal and image separation using a sparse representation of the images in the wavelet domain. We consider the problem in a Bayesian estimation framework using the fact that the distribution of the wavelet coefficients of real world images can naturally be modeled by an exponential power probability density function. The Bayesian approach which has been used with success in blind source separation gives also the possibility of including any prior information we may have on the mixing matrix elements as well as on the hyperparameters (parameters of the prior laws of the noise and the sources). We consider two cases: first the case where the wavelet coefficients are assumed to be i.i.d. and second the case where we model the correlation between the coefficients of two adjacent scales by a first order Markov chain. This paper only reports on the first case, the second case results will be reported in a near future The estimation computations are done via a Monte Carlo Markov Chain (MCMC) procedure. Some simulations show the performances of the proposed method.

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Thresholding of Wavelet Coefficients as Multiple Hypotheses Testing Procedure

Cited by 61 publications

References 2 publications

Pemilihan Parameter Threshold Optimal Dalam Estimator Regresi Wavelet Thresholding Dengan Prosedur False Discovery Rate (Fdr)

Pemilihan Parameter Threshold Optimal Dalam Estimator Regresi Wavelet Thresholding Dengan Prosedur False Discovery Rate (Fdr)

Film grain reduction on colour images using undecimated wavelet transform

Wavelet Domain Image Separation

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